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Common Core Standard HSF-BF.A.1c Questions

(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
f(x)=2x+6andg(x)=4x+2. Find (g∘f)(x).
  1. 8x+26
  2. 8x+10
  3. 6x+8
  4. 6x+12
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find (g∘f)(x) and state its domain if f(x)=3x-59x-1 and g(x)=3x+4.
  1. 9x+727x+35,  x≠-2735
  2. 9x+79x-1,  x≠19
  3. 9x+727x+35,  x≠-3527
  4. 45x-199x-1,  x≠19
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Select the possible function rules of f(x) and g(x) if (f∘g)(x)=x2-4. Choose all correct answers.
  1. f(x)=ln(x),  g(x)=ex2-4
  2. f(x)=ln(x2),  g(x)=e12x2-2
  3. f(x)=ln(x2-8),  g(x)=e12x2+2
  4. f(x)=ex-8,  g(x)=ln(x2+4)
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For f(x)=√x and g(x)=x2+8, the domain of (f∘g)(x)is:
  1. x≥0
  2. All real numbers
  3. x≤−22
  4. x≥2.828
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If f(x)=x2+3 and g(x)=√x-4 find (f∘g)(x) and state its domain.
  1. x-1,  x≥4
  2. √x2-1,  x<-1orx>1
  3. x+1,  x≥4
  4. x+1, ℝ
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If (f∘g)(x)=2|x+6|, what are possible function rules for f(x) and g(x)? There may be more than one correct answer.
  1. f(x)=√x,  g(x)=4x2+48x+144
  2. f(x)=√x2+6,  g(x)=2x
  3. f(x)=4x2+6,  g(x)=12√x
  4. f(x)=x2+6,  g(x)=2√x
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Given (f∘g)(x)=4x2−12x+9, which pair could be f and g?
  1. f(x)=2x−3,g(x)=x2
  2. f(x)=x2,g(x)=2x-3
  3. f(x)=4x+9,g(x)=2x2-3x
  4. f(x)=2x−3,g(x)=4x2-12x+9
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If f(x)=x2 and g(x)=3x-1, find (g∘f)(x).
  1. x2+3x-1
  2. 9x2-6x+1
  3. 9x2-1
  4. 3x2-1
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For f(x)=√x-1 and g(x)=x2+5, find (f∘g)(x) and state its domain.
  1. |x-1|+4,  ℝ
  2. √x2+4,  ℝ
  3. √x2+4,  -2≤x≤2
  4. √x2+4,  x≥1
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If (f∘g)(x)=x, which of the following could be possible function rules for f(x) and g(x)? Choose all correct answers.
  1. f(x)=12√x,  g(x)=2x2
  2. f(x)=14x-1,  g(x)=4x+4
  3. f(x)=ln(√x)-2,  g(x)=e2x+4
  4. f(x)=3√x-2,  g(x)=(x+2)3
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If f(x)=1x​and g(x)=x−5, find (f∘g)(2).
  1. -13
  2. 13
  3. -3
  4. 3
Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find (f∘g)(x) if f(x)=7x+1 and g(x)=-2x+34.
  1. -14x+35
  2. -14x+239
  3. 5x+35
  4. 5x+239
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Find (f∘g)(x) and state its domain if f(x)=√x+8 and g(x)=2x2-12.
  1. √2x2-4,  x≥√2
  2. √2x2-4,  x≤-√2orx≥√2
  3. √2x2-4,  x≥2
  4. √x-4,  x≥4
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If f(x)=1x​and g(x)=x−5, find (f∘g)(2).
  1. -13
  2. 13
  3. -3
  4. 3
Grade 11 Functions and Relations CCSS: HSF-IF.A.1, HSF-BF.A.1, HSF-BF.A.1c
Find the domain of the composite function f(g(x)).

f(x)=x+3
g(x)=2x+6
  1. (-∞,3)∪(3,∞)
  2. (-∞,∞)
  3. (-∞,-6)∪(-6,3)∪(3,∞)
  4. (-∞,-6)∪(-6,∞)
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For f(x)=ex+3 and g(x)=1x-2, find (f∘g)(x) and state its domain.
  1. ex+1,  ℝ
  2. e1 / (x+1),  x≠-1
  3. e(3x-5) / (x-2),  x≠2
  4. 1ex+3-2,  x≠ln(2)-3
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For f(x)=1x and g(x)=x−3, the domain of (f∘g)(x) is:
  1. All real numbers
  2. x≠0
  3. x≠3
  4. x>3
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Which composition results in h(x)=(3x+1)4?
  1. f(x)=x4,g(x)=3x+1
  2. f(x)=3x4+1,g(x)=x
  3. f(x)=3x4,g(x)=x+1
  4. f(x)=3x+1,g(x)=x4
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